Final answer:
The equation of the line that passes through the points (5,3) and (3,6) is y = -1.5x + 10.5. This is calculated based on the concept of slope and the point-slope form of the equation of a line.
Step-by-step explanation:
To find the equation of a line that passes through two given points, we first find the slope of the line (m). The slope can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the two given points.
If we use the given points (5, 3) and (3, 6), then we can substitute into our formula to find the slope first: m = (6 - 3) / (3 - 5) = - 1.5.
Once we have the slope, we then use the point-slope form of the equation of a line (y - y1 = m(x - x1)) to write the equation of the line. Substituting the slope and one of the points (I'll use the point (5,3), but you can use either), our equation becomes: y - 3 = - 1.5 (x - 5).
In slope-intercept form (y = mx + b), the equation of the line that passes through the points (5,3) and (3,6) is y = -1.5x + 10.5.
Learn more about Equation of Line